Checkerboarding with interFoam

fs82 · July 14, 2015, 09:59

Dear Foamers,

I have a very annoying problem concerning boundary conditions in multiphase flows. I like to simulate a single twodimensional bubble with interFoam. Boundary conditions are zero velocity condition at top and buttom and slip condition at the left and right wall. Alpha has zeroGradient everywhere and p_rgh fixedFluxPressure.

To generate an appropriate start solution I turned of gravity and gave the simulation some time to generate a steady solution, assuming that the bubble does not move due to missing gravity. However, after a couple of seconds my simulation crashes. The reason seems to be some oscillations (checkerboarding) visible in the horizontal velocity U at the left or right wall (velocity_slip.png). The pressure field looks strange as well (not symmetric, pressue_slip.png). I do not have a clue what is the reason for that. If I change slip to fixedValue everything is fine (velocity_fixedValue.png and pressure_fixedValue.png). I attached a testcase, if somebody wants to try it. I appreciate every help.

Best regards,
Fabian

fs82 · July 15, 2015, 08:19

Heureka, the solution is written in Ferziger, Computational Methods for Fluid Dynamics, 2008 on page 294 (section 8.8) and is related to the rhie-chow correction to avoid the checkerboarding on staggered grids. There is a minimum criteria for the Courant number of Co>0.01 and I missed it.

Gerry Kan · September 4, 2019, 04:12

Hallo Florian:

I went to my copy of Ferziger and Peric for section 8.8 (my edition was rather old so it was on a much different page number than you indicated). Here is the Zitat:

"The cell face velocity is corrected by subtracting the difference between the pressure gradient and the interpolated gradient at the cell face location. ... The correction term may be small if Ap is large. This can happen when unsteady problems are solved using very small time steps. This approach ... was developed ... and is usually attributed to Rhie and Chow (1983)."

I suppose the "small time step" part is the analog to the Courant number argument? Perhaps in the later editions it was explicitly written?

Thanks in advance, Gerry.

July 15, 2015, 08:19		#2
fs82 Senior Member Dr. Fabian Schlegel Join Date: Apr 2009 Location: Dresden, Germany Posts: 222 Rep Power: 18	Heureka, the solution is written in Ferziger, Computational Methods for Fluid Dynamics, 2008 on page 294 (section 8.8) and is related to the rhie-chow correction to avoid the checkerboarding on staggered grids. There is a minimum criteria for the Courant number of Co>0.01 and I missed it. Gerry Kan likes this.

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September 4, 2019, 04:12		#3
Gerry Kan Senior Member Gerry Kan Join Date: May 2016 Posts: 376 Rep Power: 11	Hallo Florian: I went to my copy of Ferziger and Peric for section 8.8 (my edition was rather old so it was on a much different page number than you indicated). Here is the Zitat: "The cell face velocity is corrected by subtracting the difference between the pressure gradient and the interpolated gradient at the cell face location. ... The correction term may be small if Ap is large. This can happen when unsteady problems are solved using very small time steps. This approach ... was developed ... and is usually attributed to Rhie and Chow (1983)." I suppose the "small time step" part is the analog to the Courant number argument? Perhaps in the later editions it was explicitly written? Thanks in advance, Gerry.